 reserve n,s for Nat;

theorem
  for m being Nat holds
    Triangle (n + m) = Triangle n + Triangle m + n * m
  proof
    let m be Nat;
    Triangle (n + m) = (n + m) * (n + m + 1) / 2 by Th19
      .= n * (n + 1) / 2 + m * (m + 1) / 2 + n * m
      .= Triangle n + m * (m + 1) / 2 + n * m by Th19
      .= Triangle n + Triangle m + n * m by Th19;
    hence thesis;
  end;
